I was upgrading from 12.04 to 12.10 when the battery went out on my laptop. Once I plugged it back in and booted back up it goes to the Ubuntu logo with the loading dots, but never moves past that point.

Try booting one of the earlier kernels from the grub boot menu. If you have auto login set you can force it to show the grub screen by holding down one of the <Shift> keys as soon as you see the BIOS post screen.
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fabricator4Nov 10 '12 at 21:36

1 Answer
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Sounds like you'll need to enter recovery mode - as your computer is booting, press the tab key and you should be presented with a list of options to boot from. Select the recovery mode option (this may be in a submenu called "advanced options") and wait to be presented with a menu. There should be an option to resolve package issues (I can't remember the exact title, but it will be obvious which it is). Try running this to fix the problem.